We’re used to surprises from Chilean director Pablo Larraín, whose films include the current “Jackie” and 2015’s “The Club.” His new movie, “Neruda,” is no exception. It’s a fantasia on a short period in the life of the esteemed Chilean poet and Nobel laureate Pablo Neruda — while based on fact, it’s made with a sense of freedom suggestive of poetry.

Neruda deserves a movie (this isn’t the first to be made about him), and the only question is whether the film comes anywhere close to capturing the character of this complex provocateur. He was a communist and a hedonist, a man of refinement and crudity, an artist and a huckster for revolution. “Neruda” presents all these facets, without feeling the need to judge the man, and takes a certain glee in dwelling on the contradictions.

The setting is 1948, when Neruda (portrayed with relish by Luis Gnecco) was a Chilean senator, but already famed as a poet. A stout fellow with a comfortable house and a huge appetite for the good life, he frequents brothels and parties (dressing up for one as Lawrence of Arabia). He loves his fame and enjoys taunting the Chilean establishment, a game that’s earned him the kind of enemies you don’t want to have.

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Political upheaval results in an arrest warrant that sends him underground, and his handlers will eventually decide that he should flee the country. Meanwhile, as he treks from safe house to safe house, one dedicated cop (Gael García Bernal) pursues him relentlessly — shades of Javert in “Les Misérables.” The cop hates Neruda’s politics and is far from awed by the man’s literary eminence. In a series of dry voice-overs, he reveals his disdain for the poet as a limousine liberal.

The pursuit becomes a cat-and-mouse game, and takes an unexpected — and possibly even poetic — twist when we learn a key fact about the cop that I won’t spoil. Let’s just say that this fellow, with his mustache and fedora, is the very image of a movie police officer, and seems to imagine that in his own way, he too is an artist.

Although filmmaker Larraín can seem heavy-handed or obvious at moments, he has a nicely controlled sense of irony and he’s at ease with frequent surreal touches that suit the story. He is sympathetic to the causes that Neruda represents, and while he isn’t blind to the poet’s seriously irresponsible side, he’s certainly not interested in carrying out a cinematic takedown.

This is a serious movie that often feels playful, one that has metafictional ambitions but wears them lightly. You can surrender to the enjoyment of the chase at the film’s heart, while not losing sight of Larraín’s serious aims. And if you were to, say, decide that the movie is more about the cop than the poet, I think that would be just fine with the filmmaker. That’s the spirit of the enterprise.